Ivory had some white beads and red beads in 2 bags. In Bag C, the ratio of the number of white beads to red beads was 8 : 7. In Bag D, the number of white beads was 2 times the number of red beads. Ivory transferred ²₇ of the red beads from Bag C to Bag D. The number of beads in Bag C became 78 and the ratio of the number of white beads to red beads in Bag D became 6 : 7.

1. How many red beads were transferred from Bag C to Bag D?
2. What was the number of beads in Bag D after the transfer?

	Bag C		Bag D
	White	Red	White	Red
Comparing white beads and red beads at first	8 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing white beads and red beads in the end	8 u	5 u	6 p	7 p

(a)
Total number of beads in the end for Bag C
= 8 u + 5 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of red beads that were transferred from Bag C to Bag D
= 2 u
= 2 x 6
= 12

(b)
The number of white beads in Bag D remains unchanged.  Make the number of white beads in Bag D the same.  LCM of 2 and 6 is 6. 

Increase in the number of red beads in Bag D
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 12

1 p = 12 ÷ 4 = 3

Number of beads in Bag D in the end
= 6 p + 7 p
= 13 p
= 13 x 3
= 39

Answer(s): (a) 12; (b) 39